The blunder happened at the Stonehaven Vaccination Centre in the town hall on February 1, and affected 42 people, all of whom were aged 12 years and older.
NHS Grampian has now admitted the error but said that it believed ‘the doses administered are safe and will still protect’.
However, those members of the public affected are being offered a further jab if they want one.
Commenting on the error, an NHS spokeswoman said: "We believe the doses administered are safe and will still protect.
"However, there is a very small possibility of reduced effectiveness, therefore we are offering re-vaccination if those affected want this.
"We are contacting them directly to apologise and to offer them this, according to their personal circumstances."
The health board added that everyone affected was over the age of 12, and that it did not disrupt the ongoing vaccination of five to 11-year-olds.
Additionally, an investigation into the matter has suggested it was “isolated” with no other centres affected.
“We would like to take this opportunity to apologise publicly for any distress or inconvenience,” the NHS Grampian spokeswoman added.
Latest figures show that 11.9m doses of the vaccine have been administered in Scotland with 4.14m of the population now fully vaccinated – some 75.8 per cent of the population.